There isn’t one particular place in human resources processes where companies should focus on employee engagement. That’s a long way of saying, focus on employee engagement in every single step of the way.
There is, however, a natural order. Reverse that is.
Suppose people are leaving faster than you can hire them. In that case, there really is no point in focusing heavily on employee engagement at the start of the funnel, is there? Only to see them pack up and go a couple of months later?
Start mapping employee engagement with the people who are already there. Map employee engagement efforts in a retention process, and work your way back to recruitment.